I really don't know how much scientific proof you need, but there are thousands of studies that show a completely different etiology between cancers caused by HPV-16 and those that develop due to smoking or heavy drinking.

There is a distinctive difference between the pathology of HPV-16 cancers and others.

The Head and Neck Pathology Consultation Service at the The Johns Hopkins Hospital now provides a very reliable test to detect the presence HPV-16, the most common HPV subtype to cause cancers of the head and neck. The powerful HPV-16 in situ hybridization catalyzed signal amplification method (DAKO) is highly sensitive, is applicable to formalin-fixed paraffin-embedded clinical samples, and permits direct visualization of viral sequences within tissues.

"It has now been established that the path that brings people to oral cancer contains at least two distinct etiologies; one through tobacco and alcohol, and another via the HPV virus, particularly version 16, though other versions of the virus might be implicated as the research unravels further, though any others identified as of today are considered research data artifacts and not actual causative agents. The anatomical malignancy sites associated with each pathway appear to also be different from each other. In the broadest terms they can be differentiated into these areas; HPV related cancers appear to occur on the tonsillar area, the base of the tongue and the oropharynx, and non-HPV positive tumors tend to involve the anterior tongue, floor of the mouth, the mucosa that covers the inside of the cheeks and alveolar ridges (the ridge area in which the teeth reside). The data on these two distinct etiologies is coming out of researchers more rapidly now, and there are further definitions that seem to be apparent between the two."

HPV doesn't cause all oral cancers, but it is becoming a bigger and bigger cause of them. In the 1980s about 16% of all oral cancers were HPV-related, but in the early 2000s, that number was 72%, according to researchers at the National Institutes Of Health